1) A high accurate alternating group 8-point scheme for convection diffusion problems is given. It can be used for parallel computing and is proved unconditionally stable.

2) An AGE(Alternating Group Explicit) numerical parallel method is given for a class of nonlinear evolution equation, and derived the result of unconditionally stable and parallel.

3) The alternating group iterative method for the dispersive equation with periodic boundary condition is presented.

4) In this paper, we discuss the method of Alternating Group Explicit (AGE) for solving 2-D parabolic equation, and give out the results of AGE method comparing with several fractional step methods.

5) Then on the base of this scheme, an alternating group explicit iteration ( AGEI) method is proposed and its convergence is proved.

6) The AGE(Alternating Group Explicit)numerical parallel method is given for a class of nonlinear evolution equations, and derived the result of unconditionally stable and parallel.

7) The alternating group explicit iterative method for solving the neutral parabolic equation with initial boundary conditions is given.

8) The numerical experiment shows that the alternating group explicit iterative method not only has higher precision,(http:///alternating group.html) but also is convergent faster.

9) Presents the alternating group explicit method for solving the convection equation, which is unconditionally stable.

10) The difference equations are solved by the alternating group explicit (AGE) method which is specially suitable for parallel calculations.

11) The routing algorithm for alternating group networks and shuffle-exchange permutation networks.

12) At last, in the third part we discuss the alternating group A_4 and give the character table for it.